Introduction to toric varieties

By Jean-Paul Brasselet. 2004

2,655 citations recorded by the source corpus.

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Citations in the corpus

The F-theory geometry with most flux vacua (2015, background): “In the language of toric geometry [24, 25], B2 is described by a 2D fan generated by a set of rays vi ∈ N = Z2.”
Rigidity problems in toric topology: A survey (2011, background): “A fundamental theorem in toric geometry says that there is a bijective correspondence between toric varieties of complex dimension n and fans of real dimension n, see [23] and [37] for details.”
On the $K$-theory of smooth toric DM stacks (2005, background): “See [F] for the definition of a fan.”
Torus Actions and their Applications in Topology and Combinatorics (2002, background): “Standard references in the toric geometry are Danilov'ssurvey [46] and books by Oda [105], Fulton [64] and Ewald [61].”
A compact symplectic four-manifold admits only finitely many inequivalent toric actions (2006, methodology): “blow-ups of size ǫ that are centered at points of F. Each such a blow-up creates an isolated fixed point whose moment map value is equal to that of F plus ǫ. If a Hamiltonian S 1 -action”
Motivic cell structures (2003, unknown): “For background definitions and results, see [F1].”
The orbifold cohomology ring of simplicial toric stack bundles (2005, unknown): “, ρs are rays in the complete simplicial fan Σ, if for any i, j, ρi, ρj generate a cone, then ρ1, · · · , ρs generate a cone, see [10],[15].”
Sasaki-Einstein Manifolds (2010, background): “This is a standard construction in toric geometry [46], and goes by the name of Delzant’s Theorem.”
The Nash problem on arc families of singularities (2002, methodology): “We use the notation and terminology of [8].”
Quivers with potentials and their representations II: Applications to cluster algebras (2009, background): “Let χ (Gr e ( M )) denote the Euler-Poincar´e characteristic of Gr e ( M ) (see, e.g., [14, Section 4.5]).”
Introduction to actions of algebraic groups (2010, background): “, we have isomorphisms of G-modules C ⊗ C = V (1)⊗ V (1) ∼= V (0)⊕ V (2) and one checks that the moment polytope Q(X,L) is the interval [0, 2], while Λ(X) = 2Λ ∼= 2Z.”
A generating function for all semi-magic squares and the volume of the Birkhoff polytope (2007, background): “See page 110 in [18] for more information on Todd polynomials.”
IMPANGA lecture notes on log canonical thresholds (2011, background): “This follows rather easily using some basic facts about toric varieties (for these facts, see [Ful]).”
Incidence combinatorics of resolutions (2003, background): “For a smooth toric variety X Σ , the union of closed codimension 1 torus orbits is a local subspace arrangement, in particular, the codimension 1 orbits form a divisor with normal crossings, [12, p. 100].”
Compact moduli of plane curves (2003, background): “, bk] be the expansion of r a as a Hirzebruch–Jung continued fraction ([Fu], pp.”